In 2012 David Hockney was responsible for the biggest exhibition of the year: 600,989 people visited the Royal Academy to see A Bigger Picture, a collection of his large — verging on the Brobdingnagian — paintings showing the landscape of the Yorkshire Wolds. Not long after the exhibition Hockney left Bridlington and returned to Los Angeles where he embarked on a very different project. The results are at the RA in an exhibition called 82 Portraits and 1 Still Life (until October 2).

Hockney considers the portraits (the still life was painted to fill the time when a sitter didn’t turn up) not as 82 separate works but as a single installation. They depict many of the people who matter to him, among them his brother and sister, Margaret and John, fellow painters such as John Baldessari, the starchitect Frank Gehry, the gallerists Larry Gagosian and David Juda, and the likes of Barry Humphries, Lord Rothschild and his literary collaborator Martin Gayford.

Hockney’s portraits are among the most significant works of his career and this suite marks a return to a genre he has set somewhat to one side. While he regularly refuses portrait commissions these pictures are all at his own instigation. None of the sitters knew he wanted to paint them until he asked. Once in his studio he depicted them all on identical 122x91 cm canvases, sitting on the same chair against the same blue background and teal floor (though sometimes he reverses the colours). There are no props, the sitter is the be all and end all.

The portraits’ uniformity extended to the sitting time too. “I thought I could ask people to give me three days,” Hockney says. “It is a 20-hour exposure.” Seated at an electric easel that meant he painted at the optimal level, he used the time to work directly on the canvas, with no preparatory studies but rather drawing the figure in with charcoal before turning to his paints.

Hockney’s self-imposed constraints account in part for the paintings’ lack of finish: the faces are the necessary focus of observation but the paint is rarely blended, with one shade laid on top of another. A sharp pink is the dominant colour which makes all the sitters look as though they have spent rather too long in the LA sun. Hockney’s portraits traditionally have a closeness of observation and a delicacy of draughtmanship that transmit something of the sitter’s personality. Here the sense of psychology is cursory and the subjects have a near-identical posing-for-a-portrait expression.

Hockney has admitted that he painted these pictures because he likes to be challenged. In 2000 he painted various warders at the National Gallery as a set, 12 Portraits After Ingres in a Uniform Style, to “prove” that the 19th-century Neoclassicist used some sort of optical device. His object here is less pedagogical and more experimental: an attempt to see what variety might emerge from uniformity. Not a lot is the answer. This does not invalidate the exercise. Despite a lifetime of work and recognition, Hockney still can’t sit on his hands or rest on his laurels.